# Error Term of the Taylor series of cosh

I have the Taylor series of cosh $$\sum_{n=0}^\infty \frac {x^{2n}} {(2n)!}$$

and I know that this series converges for all x, but now I want to know if the series represents the function, in other words, that the function is analytic in that interval. To do so, I should prove that the error term of the taylor expansion of cosh converges to zero, but I can't get the expression of this term.